Deep learning approaches to single-image superresolution typically use convolutional neural networks. Convolutional layers introduce translation invariance to neural networks. However, other spatial invariants appear in imaging data. Two such invariances are scale invariance, similar features at multiple spacial scales, and shearing invariance. We investigate these invariances by using weight sharing between dilated and sheared convolutional kernels in the context of multi-spectral imaging data. Traditional pooling methods can extract features at coarse spacial levels. Our approach explores a finer range of scales. Additionally, our approach offers improved storage efficiency because dilated and sheared convolutions allows single trainable kernels to extract information at multiple spacial scales and shears without the costs of training and storing many filters, especially in multi-spectral imaging where data representations are complex.